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If $\cot \theta = \frac{7}{8}$, then find the value of $\frac{(1+\sin \theta) (1-\sin \theta)}{(1+\cos\theta) (1-\cos\theta)}$.
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$\frac{(1+\sin \theta)(1-\sin \theta)}{(1+\cos \theta)(1-\cos \theta)} = \frac{1-\sin^2\theta}{1-\cos^2\theta}$ (I) (1 Mark)
$= \frac{\cos^2\theta}{\sin^2\theta} = \cot^2\theta$ (II) (1/2 Mark)
$= (\frac{7}{8})^2 = \frac{49}{64}$ (III) (1/2 Mark)
$= \frac{\cos^2\theta}{\sin^2\theta} = \cot^2\theta$ (II) (1/2 Mark)
$= (\frac{7}{8})^2 = \frac{49}{64}$ (III) (1/2 Mark)